Is it possible to use an RNN to predict a feature that is not an input feature?
Is it possible to use RNN in this case? Can it also predict features that are not part of the input features?


Yes.

No changes are required to a RNN in order to do this. All you need is correctly labelled data mapping a sequence of $x$ to correct $y$ in order to train, and of course a RNN architecture which has input vectors matching shape of $x$ and output vectors matching shape of $y$. The case where $x$ and $y$ are the same data type is just a special case of RNN design, and not a requirement.

You may need to consider some details:


If the relationship between $x$ and $y$ is complex and non-linear even accounting for accumulated hidden state during the sequence, you may need to add deeper layers. The output of the LSTM can be some vector $h$ and you can add fully-connected layers to help with predicting $y$ from $h$. This, or adding more LSTM layers, is a choice of hyperparameter that you may want to experiment with. Start with a basic LSTM to see how that goes first. 
If you wish to predict a sequence of output features that is either not the same length as the input feature sequence, or logically should come after the whole sequence (think language translation) then this may need a slight change in setup to get best results. For a predict-same-kind sequence you can feed your predicted output value into the next input, but if input and output have different data types, this will not work. Instead, you will need to have some dummy input or other setup for creating sequences of $y$. 


In your specific case the second point does not seem to apply, as you want to predict a single $y$ immediately after a sequence of $x$.